Related papers: Exact solutions of effective-mass Schrodinger equa…
Using Painlev\'e analysis, the Hirota multi-linear method and a direct ansatz technique, we study analytic solutions of the (1+1)-dimensional complex cubic and quintic Swift-Hohenberg equations. We consider both standard and generalized…
Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
We consider time-dependent nonlinear Schroedinger equations subject to smooth, lattice-periodic potentials plus additional confining potentials, slowly varying on the lattice scale. After an appropriate scaling we study the homogenization…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…
The quantum black hole model with a self-gravitating spherically symmetric thin dust shell as a source is considered. The shell Hamiltonian constraint is written and the corresponding Schroedinger equation is obtained. This equation…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
This paper concerns the homogenization of Schrodinger equations for non-crystalline matter, that is to say the coefficients are given by the composition of stationary functions with stochastic deformations. Two rigorous results of so-called…
We derive a nonsymmetrized 8-band effective-mass Hamiltonian for quantum-dot heterostructures (QDHs) in Burt's envelope-function representation. The 8x8 radial Hamiltonian and the boundary conditions for the Schroedinger equation are…
A review of a recent method is presented to construct certain exact solutions to the focusing nonlinear Schr\"odinger equation on the line with a cubic nonlinearity. With motivation by the inverse scattering transform and help from the…
Solutions of time-independent Schrodinger equation for potentials periodic in space satisfy Bloch theorem. The theorem has been used to obtain solutions of the Schrodinger equation for periodic systems by expanding them in terms of plane…
A relation between classical electrostatic fields and Schr\"odinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the…
Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation…
The exact solutions of Schrodinger equation are obtained for a noncentral potential which is a ring-shaped potential. The energy eigenvalues and corresponding eigenfunctions are obtained for any angular momentum l. Nikiforov-Uvarov method…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
The Schr\"{o}dinger equation is solved for the case of a particle confined to a small region of a box with infinite walls. If walls of the well are moved, then, due to an effective quantum nonlocal interaction with the boundary, even though…
We study the eigen-energy and eigen-function of a quantum particle acquiring the probability density-dependent effective mass (DDEM) in harmonic oscillators. Instead of discrete eigen-energies, continuous energy spectra are revealed due to…
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $\eta$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type…
In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schr\"odinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position…
By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new…